Question

what is the center of a circle represented by the equation (x + 9)^2+(y - 6)^2 = 10^2? (-9,6) (-6,9) (6,-9) (9,-6)

Explanation:

Step1: Recall circle - equation formula

The standard form of a circle equation is $(x - a)^2+(y - b)^2=r^2$, where $(a,b)$ is the center of the circle and $r$ is the radius.

Step2: Identify the center from the given equation

Given the equation $(x + 9)^2+(y-6)^2 = 10^2$, we can rewrite $(x + 9)$ as $(x-(-9))$. Comparing with the standard form $(x - a)^2+(y - b)^2=r^2$, we have $a=-9$ and $b = 6$.

Answer:

$(-9,6)$